I've posted four new papers which may be of interest to some
members of this list. They are available at
http://math.wustl.edu/~nweaver/conceptualism.html
1. "Constructive truth and circularity". I propose a
constructive interpretation of self-applicative truth and use
it to resolve the standard semantic paradoxes. This can be
read independently of my papers on mathematical conceptualism.
2. "Is set theory indispensable?" A thorough explanation of
why I feel set theory is not an appropriate foundation for
mathematics. Written for a general audience.
3. "The concept of a set". I argue that there are actually
three distinct notions of a "collection" (surveyable, definite,
and heuristic) that appear in mathematics, and that they are
governed by three different kinds of logic (classical,
intuitionistic, and minimal).
4. "Axiomatizing mathematical conceptualism in third order
arithmetic". I formulate an axiomatic system CM set in the
language of third order arithmetic which expresses the basic
principles of mathematical conceptualism, and I show how core
mathematics can be developed within this system.